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A man standing on a road has to hold his...

A man standing on a road has to hold his umbrella at `30^(@)` with the verticle to keep the rain away. He throws the umbrella and starts running at 10km/hr then he find that rain drops are hitting his head vertically, then speed of rain drops with respect to moving man:-

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When the man is rest with respect to the groudn, the rain comes to him at an angle `30^0` with the with respect to the ground. The situation when the man runs is shwon in the ure.

Here `vecv_(r,g)=` velocity o fthe rain with respect to the ground
`vecv_(m,g)=` velocity of the man with respect to the ground and `vecv_(v,m)=` velocity of the rain with respect to the man.
`We have, `vecv_(r,g)=vec_(r,m)+vecv_(m,g)` ..........i
taking horizontal components equation i. gives `vec_(r,g) sin 30^0 =v_(m,g)=10 km/h`
or `v_(r,g)=(10 km/h)/(sin 30^0)=20 km/h`
Taking vertical components, equation `i gives
`vec_(r,g) cos 30^0=v_(r,m)`
`or, v_(r,m)= (20 km/h) sqrt3/2`
`=10 sqrt3 km/h`.
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